Burke, Michael2025-09-232025-09-232025-09-232025-09-12https://hdl.handle.net/10012/22534Nearest-neighbour spin ice has been central to the study of frustrated magnetism for nearly three decades, providing a framework that reveals emergent gauge fields and monopole excitations within geometrically frustrated spins on the pyrochlore lattice. The geometry of corner-sharing tetrahedra admits only a single symmetry-equivalent nearest-neighbour bond, strongly constraining the range of allowed interactions. Recently, a new frustrated lattice of corner sharing octahedra, dubbed the octochlore lattice, has emerged as a promising platform for novel spin liquid phases. Unlike the pyrochlore, the octahedra permit distinct intra-octahedral interactions, greatly expanding the variety of realizable models. Building on the work of Szabó et al., where the spin-ice analogue was studied in a restricted region of parameter space, this thesis pursues two complementary directions. First, we investigate the spin vorticity model, in which the monopole excitations of spin ice are replaced with string-like excitations analogous to closed current loops. Second, we identify all the long-range ordered phases at the second nearest-neighbour level, fully elucidating the intra-octahedra model of Szabó et al. through an irreducible representation analysis. In doing so, we discover a novel classical U(1) analog to the celebrated X-cube model of fracton topological order. Overall, this work demonstrates that the octochlore lattice of corner-sharing octahedra constitutes a next-generation platform for three dimensional frustrated magnetism, uniquely capable of hosting exotic spin liquid phases with potential realizations in rare-earth based antiperovskites and potassium rare-earth fluorides.enfrustrationspin liquidoctochlorepyrochlorespin iceNATURAL SCIENCES::Physics::Other physics::Computational physicsNATURAL SCIENCES::Physics::Condensed matter physicsNATURAL SCIENCES::Physics::Condensed matter physics::MagnetismMonte CarloMaster Thesis